The Helmholtz Theory of the Microscope. By J. W. Gordon. 399 



and that all that marginal angle which sheds light outside the 

 aperture of the eye is at best only so much lost opportunity in the 

 use of the instrument. 



Brightness of the Image. 



It is in this connection that Helmholtz makes his first point of 

 practical importance. He points out that all this lost light con- 

 tributes nothing to the brightness of the image seen in the instru- 

 ment. It is therefore possible to use an eye-piece of higher power 

 without diminishing the apparent brightness of the image until a 

 magnifying power is reached equal to the N.M.P. of the instrument. 

 Fig. 88 illustrates this point. Here we have a given objective 

 backed by three different eye-pieces, called No. 1, No. 2, and No. 3 

 respectively. No. 1 has a low magnifying power, proportional to 

 the focal length ?\, and gives an emergent beam larger than the 



Fig. 88. 



pupil of the eye. The excess is simply thrown away, and in the 

 eye we have an image conditioned, as to scale, by the low angle 

 subtended by the semi-diameter of the pupil and, as to brightness, 

 by the area of that part of the beam which passes into the eye. 

 Eye-piece No. 2 yields a better result. Its magnifying power is 



greater in the proportion — , and the eye gets the benefit of its full 



N.A. But its image, although larger than that produced by No. 1, 

 is just as bright, for it sends a beam, of superior brightness into 

 the eye, since its beam conveys all the light coming through the 

 optical centre into the eye, and the light thrown away by objective 

 No. 1, but utilised by No. 2, is manifestly exactly proportioned to 

 the increased scale of the image. Thus the larger image is equally 

 bright — a clear gain. 



The eye-piece No. 3 has still higher magnifying power in the 



proportion — , but its use cuts down the aperture of the eye itself 



2 d 2 



